Far Eastern Mathematical Journal

To content of the issue

Solvability boundary value problem for degenerate quasilinear parabolic equation in a domain with nontube boundary

N. E. Istomina

2000, issue 1, P. 63–73

Abstract

In this paper, we consider a quasilinear parabolic equation in nontube domain, which degenerate on a solution. We suppose the essential boundedness of the derivative of the function that define the curvilinear boundary, and prove an existence and uniqness theorems for the first boundary-value problem. We use compactness methods for functions from Banach space scale. At the Preliminary part establish abstract theorems about completeness certain system of function in nontube domain.

Keywords:

Download the article (PDF-file)

References

[1] S. G. Krejn, G. I. Laptev, “Abstraktnaya sxema rassmotreniya parabolicheskix zadach v necilindricheskix oblastyax”, Differencial'nye uravneniya, 5:8 (1969), 1458–1469. [2] S. G. Krejn, “Povedenie reshenij e'llipticheskix zadach pri variacii oblasti”, Studia mathematica, 31 (1968), 411–424. [3] A. G. Podgaev, “Ob otnositel'noj kompaktnosti mnozhestva abstraktnyx funkcij iz shkaly banaxovyx prostranstv”, Sib. mat. zhurn., 34:2 (1993), 135–137. [4] A. G. Podgaev, “O svojstve kompaktnosti nelinejnyx mnozhestv i odno ego primenenie”, Neklassicheskie zadachi uravnenij matematicheskoj fiziki, IM SO AN SSSR, Novosibirsk, 1982, 134–138. [5]Zh.-L. Lions, Nekotorye metody resheniya nelinejnyx kraevyx zadach, Mir, M., 1972. [6] O. A. Ladyzhenskaya, Kraevye zadachi metematicheskoj fiziki, Nauka, M., 1973. [7] O. A. Ladyzhenskaya, N. N. Ural'ceva, Kraevye zadachi dlya linejnyx i kvazilinejnyx parabolicheskix uravnenij, Nauka, M., 1973. [8] N. E. Istomina, O korrektnosti pervoj kraevoj zadachi dlya vyrozhdayushhegosya na reshenii parabolicheskogo uravneniya v oblasti s necilindricheskoj granicej, Preprint № 5 In-ta prikl. matem. DVO RAN, Dal'nauka, Vladivostok, 2000, 24 s.

To content of the issue